9 2 Angles and Arcs Objectives To recognize

9 -2 Angles and Arcs Objectives: • To recognize major arcs, minor arcs, semicircles, and central angles. • To find measures of arcs and central angles. • To solve problems by making circle graphs.

Vocabulary • • Central Angle Arcs Minor Arc Major Arc Semicircle Adjacent Arcs Arc Length Concentric Circles • Similar Circles • Congruent Arcs

Central Angles • A central angle is an angle whose vertex is at the center of a circle.

Sum of Central Angles • The sum of the measures of the central angles of a circle with no interior points in common is 360°.

Example 1 • Determine the measure of each central angle used by the artist to draw the pie chart.

Arcs • A central angle separates a circle into arcs. • LY is a minor arc of Circle E. • LUY is a major arc of Circle E.

Semicircle • If the measure of a arc is 180°, it is called a semicircle. • Semicircles are congruent arcs formed when the diameter of a circle separates the circle into two arcs.

Definition of Arc Measure • The measure of a minor arc is the measure of its central angle. • The measure of a major arc is 360° minus the measure of its central angle. • The measure of a semicircle is 180°.

Postulate 9 -1 Arc Addition Postulate

Arc Length • Arc Length is NOT the same as the arc measure. Arc length is a distance measured in units such as centimeters. • Arc Measure is measured in degrees.

Example 2

Concentric Circles • Concentric Circles lie in the same plane and have the same center, but have different radii. • An archery or rifle target is an excellent example. • All circles are similar circles.

Congruent Circles • Circles that have the same radii are congruent circles. • Two arcs on the SAME circle with the same measure are congruent arcs.

Homework 9 -2 Worksheet